A Bayesian non-parametric Potts model with application to pre-surgical FMRI data
The Potts model has enjoyed much success as a prior model for image segmentation. Given the individual classes in the model, the data are typically modeled as Gaussian random variates or as random variates from some other parametric distribution. In this article, we present a non-parametric Potts mo...
Gespeichert in:
| Hauptverfasser: | , , , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
2013
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| In: |
Statistical methods in medical research
Year: 2013, Jahrgang: 22, Heft: 4, Pages: 364-381 |
| ISSN: | 1477-0334 |
| DOI: | 10.1177/0962280212448970 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1177/0962280212448970
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| Verfasserangaben: | Timothy D Johnson, Zhuqing Liu, Andreas J Bartsch and Thomas E Nichols |
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| 520 | |a The Potts model has enjoyed much success as a prior model for image segmentation. Given the individual classes in the model, the data are typically modeled as Gaussian random variates or as random variates from some other parametric distribution. In this article, we present a non-parametric Potts model and apply it to a functional magnetic resonance imaging study for the pre-surgical assessment of peritumoral brain activation. In our model, we assume that the Z-score image from a patient can be segmented into activated, deactivated, and null classes, or states. Conditional on the class, or state, the Z-scores are assumed to come from some generic distribution which we model non-parametrically using a mixture of Dirichlet process priors within the Bayesian framework. The posterior distribution of the model parameters is estimated with a Markov chain Monte Carlo algorithm, and Bayesian decision theory is used to make the final classifications. Our Potts prior model includes two parameters, the standard spatial regularization parameter and a parameter that can be interpreted as the a priori probability that each voxel belongs to the null, or background state, conditional on the lack of spatial regularization. We assume that both of these parameters are unknown, and jointly estimate them along with other model parameters. We show through simulation studies that our model performs on par, in terms of posterior expected loss, with parametric Potts models when the parametric model is correctly specified and outperforms parametric models when the parametric model in misspecified. | ||
| 650 | 4 | |a decision theory | |
| 650 | 4 | |a Dirichlet process | |
| 650 | 4 | |a FMRI | |
| 650 | 4 | |a hidden Markov random field | |
| 650 | 4 | |a non-parametric Bayes | |
| 650 | 4 | |a Potts model | |
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| 700 | 1 | |a Nichols, Thomas E. |e VerfasserIn |4 aut | |
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